COMBINATORIAL STRUCTURES IN SPIN MODELS: ALGORITHMS FOR GENERATION OF OPERATOR MATRICES
Adam Mickiewicz University, Institute of Physics
Umultowska 85, 61-614 Poznań, Poland
e-mail: florek@spin.amu.edu.pl
DOI: 10.12921/cmst.2001.07.01.41-54
OAI: oai:lib.psnc.pl:514
Abstract:
Two combinatorial algorithms, generation of ordered partitions of N with no more than m parts and decompositions of N-element set into subsets with cardinalities given by a partition [k] = [k0 k1… km-1] are presented and their possible applications to finite (mesoscopic) spin systems are indicated. The flow charts, listings, and results of test runs are provided.
References:
[1] S. Bucikiewicz, W. Florek, CMST, this volume.
[2] G. Kamieniarz, R. Matysiak, W. Florek, S. Walcerz, J. Magn. Magn. Mater., 203, 271 (1999).
[3] E. N. Reingold, J. Nivergelt, N. Deo, Combinatorial Algorithms. Theory and Practice, Prentice Hall, Engelwood Cliffs NJ, 1977.
[4] W. Lipski, Combinatorics for Programmers. Polish Sci. Publ. (PWN), Warsaw, 1982 [in Polish].
[5] A. Kerber, Algebraic Combinatorics via Finite Group Actions. B I Wissenshaftsverlag, Mannheim-Wien-Zürich, 1991.
[6] D. Gatteschi, A. Caneschi, L. Pardi, R. Sessoli, Science, 265, 1054 (1994); A. Lascialfari,
D. Gatteschi, A. Cornia, U. Balucani, M. G. Pini, A. Rettori, Phys. Rev. B, 57, 1115 (1998);
A. Caneschi, D. Gatteschi, C. Sangregorio, R. Sessoli, L. Sorace, A. Cornia, M. A. Novak,
C. Paulsen, W. Wernsdorfer, J. Magn. Magn. Mater., 200, 182 (1999).
Two combinatorial algorithms, generation of ordered partitions of N with no more than m parts and decompositions of N-element set into subsets with cardinalities given by a partition [k] = [k0 k1… km-1] are presented and their possible applications to finite (mesoscopic) spin systems are indicated. The flow charts, listings, and results of test runs are provided.
[1] S. Bucikiewicz, W. Florek, CMST, this volume.
[2] G. Kamieniarz, R. Matysiak, W. Florek, S. Walcerz, J. Magn. Magn. Mater., 203, 271 (1999).
[3] E. N. Reingold, J. Nivergelt, N. Deo, Combinatorial Algorithms. Theory and Practice, Prentice Hall, Engelwood Cliffs NJ, 1977.
[4] W. Lipski, Combinatorics for Programmers. Polish Sci. Publ. (PWN), Warsaw, 1982 [in Polish].
[5] A. Kerber, Algebraic Combinatorics via Finite Group Actions. B I Wissenshaftsverlag, Mannheim-Wien-Zürich, 1991.
[6] D. Gatteschi, A. Caneschi, L. Pardi, R. Sessoli, Science, 265, 1054 (1994); A. Lascialfari,
D. Gatteschi, A. Cornia, U. Balucani, M. G. Pini, A. Rettori, Phys. Rev. B, 57, 1115 (1998);
A. Caneschi, D. Gatteschi, C. Sangregorio, R. Sessoli, L. Sorace, A. Cornia, M. A. Novak,
C. Paulsen, W. Wernsdorfer, J. Magn. Magn. Mater., 200, 182 (1999).
